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Understanding the Mantel Test for Matrix Correlation Analysis in Ecological Studies

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The Mantel Test evaluates the correlation between distance or dissimilarity matrices, useful in ecology and genetics. It assesses if there is a relationship by comparing matrices through the Pearson correlation coefficient, ranging from -1 to 1. A significant result indicates that the correlation between the matrices is different from zero, verified through randomizations (recommended 10,000). The Partial Mantel Test allows control for a third variable. Use cases include studying community structure changes, genetic and geographic distances, and examining ecological relationships.

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Understanding the Mantel Test for Matrix Correlation Analysis in Ecological Studies

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  1. Mantel Test Evaluates correlation between distance, similarity, correlation or dissimilarity matrices Null: no relationship between matrices Pearson correlation (r) can be used to measure strength of relationship r ranges from -1 to 1

  2. Test for Significance • Evaluates the results from repeated randomizations • If randomizations frequently produce a correlation stronger or as strong as the original data little evidence that correlation differs from zero. • Order of randomization is important - order of row and columns are shuffled for one matrix

  3. Randomization cont. • Mantel’s Z statistic is computed after each permutations and a distribution is created • Z statistic from nonrandomized data is compared to the distribution of the shuffled matrix. • If null is true, Mantel statistic will fall near the middle of the reference distribution • 10,000 randomizations is recommended • wij = connectivity or Euclidean distance matrix and xij = dissimilarity or distance matrix n Z= n wijxij i =1 j=1 i=j j=i

  4. What is really computed? • Is the relationship between distance measures not the raw data

  5. When to use Examples: • Two groups of organisms form same set of sample units • Community structure before and after disturbance • Genetic distance and geographic distance • Ecological distance and geographic distance

  6. Partial Mantel Test • Quantifies the relationship between two matrices while controlling for the effects of a third one.

  7. Problem with Mantel • Relationship is a global outcome for all variables • Can pick out which variables have the most influence • Solution: Use ordination: CCA and RDA

  8. Vegetation Types • Reference Rosemary Scrub Semi-improved Pasture Disturbed Scrub

  9. Sampling Design Macroplot Subplot Quadrat 16 X 16 m 2 x 2 m 40 x 40 cm

  10. Data Matrices Seed Bank Horn-Morisita Percent Cover Bray-Curtis X-Y Coordinates Euclidean

  11. Mantel Test in R • ecodist and vegan package • Both matrix must be identical and contain x and y coordinates • Must choose an appropriate distance measure: • Bray-Curtis - Manhattan • Euclidean • Morisita • Horn-Morisita

  12. Results

  13. Pasture

  14. Disturbed Scrub

  15. Rosemary Scrub

  16. Results

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